We cordially invite you to the
Ökonometrisches Forschungsseminar / Econometric Research Seminar
(M. Deistler, A. Jumah, A. Weber)
on Thursday, May 10, 2001, at 9.15 a.m.
Institute for Advanced Studies, SZ VI,
Stumpergasse 56, A-1060 Vienna
held by
Gabriela DE RAAIJ and Burkhard RAUNIG (Österreichische Nationalbank)
"Evaluating Density Forecasts of Stock Market Returns"
Abstract:
The paper deals with the evaluation of density forecasts, which have become
quite popular in economics and finance. We use two probability integral
transformations to evaluate such forecasts. The first transformation
implies that the realizations transformed with respect to the forecasted
densities of a stochastic process should be identically uniformly
distributed if the density forecasts coincide with the densities underlying
the true data generating process. The second transformation generates data
that are identically normally distributed if the correct densities are
forecasted. The second transformation enables us to apply standard
statistical techniques to test for identically normally distributed data
and hence for the quality of density forecasts.
We use the methodology to evaluate density forecasts for daily returns of
three stock market indices (S&P 500, DAX and ATX). Various models to
forecast conditional densities are investigated. We consider the
conditional normal distribution where the variances are estimated by moving
averages or exponentially weighted moving averages, scaled t distributions
and GARCH(1,1) variants with normally and t-distributed errors,
respectively. In- and out-of-sample results for the density forecasting
models are examined. Using the proposed methodology we find that GARCH
models with t-distributed errors perform best in sample as well as out of
sample. We are also able to demonstrate that certain misspecifications of a
forecasting model are quite naturally reflected in the transformed series
used for density forecast evaluation.
Key words: Density forecasting, Forecast evaluation, Risk management
JEL Classification: G10, C52, C53
With best regards,
Nina Gritzky
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Mag. Nina Gritzky
IHS - Institut für Höhere Studien / Institute for Advanced Studies
Stumpergasse 56
A-1060 Wien (Vienna), Austria
Tel: +43/1/59 991-145
Fax: +43/1/59 991-163
e-mail: gritzky(a)ihs.ac.at
WWW:
http://www.ihs.ac.at